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Math Help - parametrization and stokes's theorem

  1. #1
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    parametrization and stokes's theorem

    Let F (x, y, z) = 6yx^2i + 2x^3j + 6xyk, and C be the curve of intersection of the hyperbolic paraboloid z = y^2 - x^2 and the cylinder x^2 + y^2 = 25 oriented counterclockwise as viewed from above.
    (i) Obtain a parametrization of the curve C and use the result to evaluate \int_{C} F \cdot dr.
    (ii) use Stokes's Theorem to evaluate \int_{C} F \cdot dr.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    See the attachment.

    If you have trouble visualising the curve you can see the animation

    motion on a saddle on my web site Calculus 3
    Attached Files Attached Files
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